Prediction of the influence of processing parameters on synthesis of Al2024-B₄C composite powders in a planetary mill using an artificial neural network

3.1 Collecting the experimental data

In this study, the alteration of particle size and particle hardness of Al2024-B₄C powders produced by the MA method was modeled by the ANN. To examine the effect of reinforcement size, reinforcement ratio, and milling time on the particle size and particle hardness of the Al2024-B₄C composite powder, the experimental data were grouped into training and test data. The training data were used in the forecast model, as shown in Table 2.

Different models have different network structures, and thus, different learning parameters were examined in the training period. To test the performance of the networks, the models were tested with data that were not used in the training set. This method made it possible to obtain the most precise results. The estimated values from the tests were then compared to the measured values. In designing ANNs and selecting definite design parameters, the selection can be more or less subjective, but it is very important to achieve optimally the best neural network performance. The information that determines the performance of the network is obtained by the aid of diverse identification methods that attempt to minimize the difference between the output calculated by the ANN and the desired output. From the well-known and widespread identification tools, the root mean squared error (RMSE) and the mean absolute percentage error (MAPE) values are calculated from Eqs. (3) and (4) [22]. Models that produce the best estimated values were selected as the forecasting models.

where t_i is the real value, td_i is the model prediction value, and N is the number of testing data.

Table 2 shows the actual values, percentage error rates, RMSE, and MAPE calculated using the estimated models.

3.2 Neural network architecture

Figure 4 shows the ANN model containing one input layer, two hidden layers, and one output layer. The selected ANN model represents the prediction model that produced the closest values to the measured values for the particle size. The reinforcement size (μm), reinforcement ratio (wt%), and milling time were used as the input variables, while the particle size and particle hardness were used as the output variables in the ANN models. The processing element numbers (neurons) of the hidden layers were 6 and 6 for the model in Figure 4.

Figure 4

ANN architecture selected as prediction model for the particle size (μm) and particle hardness (Hv).

The number of neurons in the input and output layers is usually selected on the basis of the number of parameters affecting the process and the complexity of the relationships existing between them. There is no rigid rule for calculating the number of neurons in the hidden layers. Normally, the numbers of neurons or processing elements in the hidden layer are selected taking into account the number of data points available for training the network and also the complexity of the relationship existing between the input and the output parameters [23]. The minimum error was obtained at six nodes at the first hidden layer and six nodes at the second hidden layer.

3.3 Network training and testing

A forward and backward feed propagation multilayer ANN was used for solving problems, and the network training and testing was carried out using the MATLAB software package. In this study, the hyperbolic tangent sigmoid function (tansig) [Eq. (2)] and the linear transfer function (purelin) were used as the activation transfer functions, the resilient back propagation function (trainrp) was used as the training algorithm, the gradient descent with a momentum back propagation algorithm (traingdm) was used as the learning rule, and the mean square error (MSE) was used as the performance function. To ensure an equal contribution of each parameter in the model, the training and test data sets were normalized (-1, 1 range) due to the use of the hyperbolic tangent sigmoid function in the model and network, which allowed the data to be translated into the original value with a reverse normalizing process for the interpretation of the results. The normalization (scaling) operations were carried out using Eq. (5):

where X_norm is the normalized value, X is the true value of the variable, X_min is minimum value of the data set, and X_max is the maximum value of the data set.

It was decided that the 0.001 targeted error values would be sufficient for the training of the ANN. Figure 5 shows the iteration-dependent error variation quantity for an ANN selected for the green density, sintered density, and hardness values (Figure 5). The number of epochs after which the training models were stopped is 42.

Figure 5

Iteration-dependent error variation graphic of the ANN.

4.1 Effect of reinforcement properties on the milling system

In order to determine the effects of both particle size and weight percentage of B₄C particles on the milling process, two new models were developed (Figure 6A and B). Figure 6A shows the effect of coarse B₄C particle on the milling process. In the first stage of milling, the ductile particles undergo deformation, while brittle particles undergo fragmentation. However, the fragmentation of B₄C particles was very limited in this stage. Flattened Al2024 particles were trapped between the B₄C particles (Figure 6A). As can be seen in Figure 6A, hard B₄C particles create microcracks on flattened ductile particles due to deformation and cutting effect of hard particles. Cutting effect can be defined as forcing ductile particles to fragmentation. The cutting effect of hard B₄C particles prevented the excessive cold welding process between ductile Al2024 powders, and thus, the particle size of milled powders showed a small reduction in the first stage of milling. The cutting effect of hard B₄C particles continued until work hardened the ductile Al2024 powders and fragmented reinforced particles. In the second stage of milling, the fracture process increased due to work hardening mechanism, causing dispersion of hard B₄C particles in the matrix powder. Homogeneous particle morphology, particle size, and dispersion of B₄C particles in the final stage of milling (steady state) were obtained.

Figure 6

The milling models showing the effect of reinforcement size on the milling process: (A) coarse brittle powders, (B) fine brittle powders.

Figure 6B shows the effect of fine B₄C particles on the milling process. In the first stage of milling, the morphology of ductile Al2024 powders changed and flattened particles were formed due to ball-powder-ball collisions. Moreover, all reinforcement particles were embedded into the flat and ductile Al2024 particles (Figure 6B) in this stage. After the cold welding of ductile and brittle particles, the milling process continued through ball-powder (ductile+hard particles)-ball collisions. B₄C particles embedded into the ductile Al2024 particles created a deformation effect rather than a cutting effect. In the second stage of milling, the local deformation of Al2024 matrix powders increased due to fine B₄C particles embedded into the Al2024 powders, and so fracture toughness of milled powders was reduced and the fracturing process was enhanced [24]. In the final stage of milling, it was observed that there was a balance between the fracture and cold welding processes.

Particle sizes of Al2024 and composite powders for different B₄C size, B₄C content, and milling time are shown in Figure 7A and B. The effect of milling time and reinforcement ratio on the particle size of milled powders has been previously studied by Razavi Tousi et al. [25], Abdoli et al. [26], Fogagnolo et al. [27], and Alizadeh and Aliabadi [28] in the case of monolithic and composite powders. In these studies, it has been commonly stated that hard particles, such as Al₂O₃, SiC, AlN, and B₄C, have an important effect on the change of the particle size and morphology of the composite powder. This can be explained by the effect of the high volume fraction of ceramic particles on the welding behavior of the ductile particles. The ceramic particles are embedded between the ductile particles, thus preventing cold welding from occurring. Another reason is the local deformation of the ductile particles in the vicinity of ceramic particles during the milling process. The result of this local deformation is increase in the hardness of powders and decrease in the cold welding [25]. As can be seen in Figure 6A and B, the cutting effect of coarse particles was as important as the embedding process of fine particles for the change in particle size. It was determined that the initial size of coarse B₄C particles was 10 times larger than the initial size of fine B₄C particles, although the difference between sizes of composite powders was very little during the milling process. Average particle size of composite powders after 2 h of milling was 38 μm (C20) and 35 μm (F20) for the same B₄C content (20 wt%) and different reinforcement size. The coarse B₄C particles were rarely embedded into the ductile Al2024 particles, whereas fine B₄C particles were fully embedded into the ductile Al2024 particles up to 2 h of milling. This result cannot be explained based on the work of previous investigation because the reduction of particle size was explained with the embedding process by these studies [25–28]. One of the most important reasons for the close particle size for different initial size of B₄C particle was a cutting effect created by hard ceramic particles.

Figure 7

Effect of milling time and B₄C content on the average particle size: (A) Al2024-B₄C_Coarse, (B) Al2024-B₄C_Fine.

The initial morphology of the B₄C particles was angular or polygonal in shape, while the Al2024 powder had ligament morphology and an irregular shape. It was clear that the particle size and morphology changed with increasing milling time. Cold welding increases the particle size, while fracturing reduces the size [29]. In the first stage of milling, the particles exhibit significant plastic deformation due to the mechanical milling process, and thus the shape of reinforced and unreinforced powders changed from ligament to flake for the milling performed. In other words, the plastic deformation of the soft matrix powder began quickly within a short milling time, resulting in a change in the morphology from ligament-like to flattened shape [5]. Mixing with the ceramic particles could also increase the rate of fracturing of milled powders. Hence, with continued milling the particles get work hardened and become more brittle, and their fracture leads to a reduction in particle size. In the final stage of milling, a balance was established between the cold welding and fracturing processes and a steady-state situation was obtained. These results clearly showed that the particle size was stabilized and did not change with further milling [29].

4.2 Training and validating of ANN

The ANN was trained and implicated using a fully developed feed forward back propagation neural network. In this study, 49 data were generated by varying the reinforcement size and reinforcement ratio and milling time. For each experiment, the particle size and particle hardness were measured. Out of the total data generated from experiments, 33 data sets were used to train the ANN, and 16 sets of data were selected for the validation of the optimum ANN. The developed ANN consists of three input nodes, namely, (a) reinforcement size (μm), (b) reinforcement ratio (wt%), and (c) milling time (h). The two neurons in the output layer represent the two output parameters, namely, particle size and particle hardness. The numbers of neurons in the hidden layer are determined by trial and error during training.

The predicted values, deviation, and percent error for the particle size and particle hardness are provided in Tables 2 and 3. The ANN was tested for accuracy using the test values (Table 3) selected from the experimental results that were not used during the learning processes. In most cases, the neural network prediction is very close to the actual value. However, several values are not as close as others, which is due to the errors caused by the material, the measurements, and the process parameters. However, these errors could be neglected given that the learning level of the ANN is 96%. This study revealed that the predictions made using the ANN produced more accurate results.

Figures 8 and 9 show the relationship between the real and calculated values obtained using the prediction models. The MAPE is used to evaluate the performance of the proposed ANN as a prediction technique. The MAPE values are 4.289% for particle size and 3.143% for particle hardness. With respect to the results obtained from the plots of the ANN prediction, the highest MAPE value of 4.289% demonstrates that the network effectively generates sensitive results.

Figure 8

Relationship between experimental and ANN predicted values for the testing data set: (A) particle size (μm), (B) particle hardness (Hv).

Figure 9

Comparison of the real and calculated values for testing data set: (A) particle size (μm) and (B) particle hardness (Hv).

A comparison of the measured and predicted (ANN) particle size and particle hardness at the training and testing stage is provided in Figure 9. From these comparison charts, it can be clearly observed that the ANN is properly trained and shows consistency in predicting the properties of the powder. A comparison between the measured and predicted composite powder properties at the testing stage indicates a high correlation. In other words, the results of the comparison plots indicate the similarities between the experimental study and the ANN model and support the reliability of the model. The comparison diagrams reveal that the slope and intercept of the regression equations for the outputs are very close to 1 and 0, respectively.

The validity of the prediction models was proven by means of the determination of the predictive mean absolute error (MAPE) and correlation coefficient (R). RMSE is also known as the fit standard error and the standard error of the regression. An RMSE value closer to zero indicates a better fit. Figure 8 shows the regression analysis of the ANN model for the particle size and particle hardness. The correlation coefficient obtained was 0.99, indicating good agreement between the experimental results and the model prediction (R_{particle size}=0.99538, R_{particle hardness}=0.98948). The statistical results, namely, the RMSE and the MAPE, are within an acceptable range and meet the integrity of the ANN learning and testing stages. Thus, reasonable agreement between the predicted and experimental data supports the accuracy of the model.